1. Field of the Invention
The present invention relates to an initial synchronization method and apparatus, and more particularly to an initial synchronization method and apparatus for estimating timing error and frequency offset.
2. Related Art
Timing recovery and carrier frequency offset (CFO) compensation are crucial for any wireless communication application. Pseudo-noise (PN) sequences are often employed to serve as training preambles for the purpose of time synchronization in a variety of wireless communications. Although PN sequences can support high-resolution time synchronization because of their good correlation properties by taking advantage of PN matched filtering (PN MF), they are vulnerable to the CFO [3]-[8]. The vulnerability is mainly because the cross-correlation between the received signal and a locally generated PN sequence can be destroyed by undesired phase increments (or decrements) in the correlation period of the PN MF, in which a non-negligible CFO exists.
The CFO occurring in mobile communications is mainly caused by mismatch of the local oscillator at the receiving end, meanwhile the relative movement, however, leads to a Doppler spread, which is inevitably caused by many reflections from surroundings. The CFO is more dominant than a Doppler frequency even in a very-high-mobility environment.
A particular synchronization burst, called a dual-chirp signal, was originally discussed in Geostationary Earth Orbit (GEO) Mobile Radio (GMR) mobile-satellite communications and its properties have been investigated in detail in a previous work and its references. Several studies have employed chirp signals as training sequences for time-domain (TD) synchronization or CFO estimation in wireless orthogonal-frequency-division-multiplexing (OFDM) communication systems.
Zadoff-Chu (ZC) sequences, which are also chirp-like sequences, have been employed as random access preambles, primary synchronization sequences for cell search and reference sequences for channel estimation (CE) in the Third-Generation Partnership Project (3GPP) Long-Term Evolution, which is a mobile communication specification. The synchronization mechanisms studied in the previous works generally utilize autocorrelation or cross-correlation evaluation to estimate the time error and CFO. However, rigorous analyses based on statistical derivations have been omitted, especially in multi-path fading environments.